Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is :

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is :

A
170
B
190
C
180
D
210

Solution:

Since, 20 pillars are connected by beams with all its non adjacent pillars.

$∴$ Total number of beams $=^{20} C_{2} - 20$

$= \frac{20!}{18! 2!} - 20 = \frac{20 \times 19}{2} - 20 = 170$

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Solution:

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